Let \( \mu _{\beta }\)  be the sine\( _{\beta }\)  random point field [1]}.
Replacing \( \mu \)  by \( \mu _{\beta }\)  (\( \beta = 1,4\) ),
we consider the Dirichlet form \( \mathcal {E} \)  in Eq. (REF ) for \( \beta =1,4\) .
The unlabeled diffusion has been constructed for \( \beta = 1,4\)  [2]}, and
the associated labeled process \( \mathbf {X}= (X^i)_{i\in \mathbb {N}}\) 
satisfies ISDE (REF ) for \( \beta = 1,2,4\)  [3]}.
These cases have been proved as examples of the general theory developed in various papers [4]}, [3]}, [2]}, [7]}.
